ARUP; ISBN: 978-0-9562121-5-3 - CMBBE 2012 - Cardiff University

3.3 Computational study
The 3D model was meshed with unstructured tetrahedral grid and a sensitivity analysis
was conducted doubling the number of elements and ensuring that pressure drop across
the model did not change more than 2%. The mesh chosen for the in-silico study
contained around 300,000 elements (Fig. 4, left). As in the experimental setup, the 3D
model was coupled to the LPN comprising the UB, LB and P impedances merging into
the constant pressure generator (16 mmHg), while excluding the additional compliance
placed at the inlet. In fact, since the VAD flow signal was not measured, the inflow
boundary condition (Qin) was assigned as the Fourier series of the velocity waveform
derived from the sum of the three outflows (QUB, QLB, QP) recorded in-vitro. The C and
R values, experimentally measured and extrapolated, respectively, were implemented in
the LPN, resulting in a system of three ordinary differential equations and three
algebraic equations. A multiscale coupling approach [8] was adopted imposing timevarying
uniform pressures, calculated by the LPN, at each 3D outlet and flow rates,
averaged over the sections, to the LPN. Blood was assumed as an incompressible
Newtonian fluid with density of 1060 kg/m 3 and dynamic viscosity of 3.6·10 -3 Pa·s [12].
A pulsatile simulation was run using commercial software (Fluent 12.1.4, ANSYS, Inc.,
Canonsburg, PA, USA), with the implicit Euler method as the time integration
technique for solving Navier-Stokes equations in the 3D domain and the explicit Euler
method for solving the LPN system. Time step was fixed at 5·10 -5 s and four cycles
were considered sufficient for stability of the solution. The average time to complete
one cardiac cycle was about 24 hours, using an Intel® Core i7 (3GHz) personal
computer. Pressure was monitored and averaged over three cross-sections of the 3D
model, corresponding to the same locations of the pressure ports. All mean values were
calculated over three cycles to compensate the variability of the experimental data.
4. RESULTS AND DISCUSSION
As expected, steady flow measurements performed on the valves indicated a non-linear
behavior (∆P ≈ αQ 2 + βQ, being α and β constants, ∆P and Q the pressure drop and flow
across the valve, respectively). Values of α and β coefficients for each non-linear
resistance are displayed in Figure 2 in the fitting curve equations.
Fig. 2 Non-linear pressure drop-flow
relationships of the valves used in-vitro. The
blue curve is relative to the upper and lower
body resistances (RUB, RLB), the red curve to
the pulmonary resistance (RP).
Figure 3 shows the flow (left) and pressure
(right) tracings recorded during the in-vitro
and in-silico simulations. Overall,
computational flows (dashed lines)
satisfactorily matched the experimental
data (solid lines), in terms of both
waveforms and mean values. A maximum
difference in mean flow of 17% was measured at the UB outlet (0.77 vs 0.90 L/min, invitro
vs in-silico), where the computational model reported higher perfusion than in-